A332234 Least integer t such that every binary word of length t+1 contains a reversed split occurrence of an n-overlap.

2, 4, 15, 46

Offset

0,1

Comments

An "n-overlap" is a word of the form xxx', where x is a nonempty word of length at least n, and x' is a prefix of x of length n. Thus, for example, abcdabcdab is a 2-overlap. A reversed split occurrence of a pattern p is a word of the form xyz where zx matches the pattern.

For n = 0,1,2,3 words achieving the bound a(n) are as follows:

n = 0: 01

n = 1: 0011

n = 2: 010001100111001

n = 3: 0010100110100011111000111010000011101010001100

Links

Table of n, a(n) for n=0..3.

D. Gabric and J. Shallit, Avoidance of split overlaps, arxiv preprint arXiv:2002.01968 [cs.DM], February 5 2020.

Crossrefs

Cf. A332235.

Sequence in context: A072206 A296255 A277508 * A316726 A308345 A280065

Adjacent sequences: A332231 A332232 A332233 * A332235 A332236 A332237

Keyword

nonn,more

Author

Jeffrey Shallit, Feb 07 2020

Status

approved